The accurate estimation and forecasting of volatility is of utmost importance for anyone who participates in the financial market as it affects the whole financial system and, consequently, the whole economy. It has been a popular subject of research with no general conclusion as to which model provides the most accurate forecasts. This thesis enters the ongoing debate by assessing and comparing the forecasting performance of popular volatility models. Moreover, the role of key parameters of volatility is evaluated in improving the forecast accuracy of the models. For these purposes a number of US and European stock indices is used. The main contributions are four. First, I find that implied volatility can be per se forecasted and combining the information of implied volatility and GARCH models predict better the future volatility. Second, the GARCH class of models are superior to the stochastic volatility models in forecasting the one-, five- and twenty two-days ahead volatility. Third, when the realised volatility is modelled and forecast directly using time series, I find that the HAR model performs better than the ARFIMA. Finally, I find that the leverage effect and implied volatility significantly improve the fit and forecasting performance of all the models.